Making use of the cube root table, find the cube root
34.2
The number $34.2$ could be written as $\frac{342}{10}$.
Now
$\sqrt[3]{34.2}=\sqrt[3]{\frac{342}{10}}=\frac{\sqrt[3]{342}}{\sqrt[3]{10}}$
Also
$340<342<350 \Rightarrow \sqrt[3]{340}<\sqrt[3]{342}<\sqrt[3]{350}$
From the cube root table, we have:
$\sqrt[3]{340}=6.980$ and $\sqrt[3]{350}=7.047$
For the difference $(350-340)$, i.e., 10 , the difference in values
$=7.047-6.980=0.067 .$
$\therefore$ For the difference $(342-340)$, i.e., 2 , the difference in values
$=\frac{0.067}{10} \times 2=0.013$ (upto three decimal places)
$\therefore \sqrt[3]{342}=6.980+0.0134=6.993$ (upto three decimal places)
From the cube root table, we also have:
$\sqrt[3]{10}=2.154$
$\therefore \sqrt[3]{34.2}=\frac{\sqrt[3]{342}}{\sqrt[3]{10}}=\frac{6.993}{2.154}=3.246$
Thus, the required cube root is 3.246.
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